RATIO OF APERTUKE AND FOCAL LENGTH. 101 



recognition of the details, a faultless magnification of 400, and for 

 convenient observation, one of 600 700 diameters. The errors of 

 workmanship of the instrument raise these figures somewhat 

 higher, probably to 500 and 800. The simple perception of 

 the image takes place, then, with an eye-piece amplification of 



about '4. The amplification by the objective is still j- = 125 ; 



for its focal length, we get from the formula 



p* 190 



/ = -=- - ,-if p* = 190 mm., \ = 1*5 mm. 



Should a somewhat higher eye-piece amplification be admissible, 

 say five linear, then the magnifying power of the objective = 100, 

 and its focal length 1*9 mm. In both cases the further surface- 

 extension of the image, for convenient observation, may be effected 

 by means of deep eye-pieces. 



Similarly, for an immersion objective, whose angle of aperture 

 = 180 in air, we get half a wave-length, or *28 mic., for the 

 absolute limit of differentiation. The magnification required for 

 accurate delineation of such details is in round numbers 430, and, 

 in consequence of the unavoidable errors of construction in the 

 present state of workmanship, this may be increased to 600 or 700. 

 With an eye-piece amplification of four linear, we get for the 

 objective a magnifying power m = 150 to 175, from which /can 

 be estimated, according to the suppositions above given, at the 

 still considerable magnitude of 1*26 to TO 9 mm. If, then, the 

 combined amplification were 800, which is certainly sufficient, the 

 focal length would still not be perceptibly less than 1 mm. We 

 'conclude that objectives of -gV, &c., can possess no advantage 

 beyond the very doubtful one of useless amplification. Conse- 

 quently, we shall not be wrong in estimating all amplifications 

 exceeding 1,500 to 2,000 as valueless for scientific purposes. 



dimension perceptibly greater (often as much as 150 mic.) is usually necessary 

 with dioptric or interference images. In many cases' an amplification at least 

 twice as great is required for convenient observation ; this would therefore 

 amount to 1,000. 



